Problem: Rewrite as a simplified fraction. ${2.8\overline{24} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2824.2424...\\ 10x &= 28.2424...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2796}$ ${x = \dfrac{2796}{990}} $ ${x = \dfrac{466}{165}} \text{or} {2 \dfrac{136}{165}}$